%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL902+1 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:00:00 AM UTC 2026
% Result : Theorem 0.13s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 48 ( 34 unt; 0 def)
% Number of atoms : 66 ( 21 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 35 ( 17 ~; 11 |; 2 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 75 ( 9 sgn 23 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos_02,axiom,
! [A,B] : '+'(A,B) = '+'(B,A),
file('theBenchmark.p',sos_02) ).
fof(sos_03,axiom,
! [A] : '+'(A,'0') = A,
file('theBenchmark.p',sos_03) ).
fof(sos_04,axiom,
! [A] : '>='(A,A),
file('theBenchmark.p',sos_04) ).
fof(sos_05,axiom,
! [X0,X1,X2] :
( ( '>='(X1,X2)
& '>='(X0,X1) )
=> '>='(X0,X2) ),
file('theBenchmark.p',sos_05) ).
fof(sos_06,axiom,
! [X3,X4] :
( ( '>='(X4,X3)
& '>='(X3,X4) )
=> X3 = X4 ),
file('theBenchmark.p',sos_06) ).
fof(sos_07,axiom,
! [X5,X6,X7] :
( '>='('+'(X5,X6),X7)
<=> '>='(X6,'==>'(X5,X7)) ),
file('theBenchmark.p',sos_07) ).
fof(sos_08,axiom,
! [A] : '>='(A,'0'),
file('theBenchmark.p',sos_08) ).
fof(sos_09,axiom,
! [X8,X9,X10] :
( '>='(X8,X9)
=> '>='('+'(X8,X10),'+'(X9,X10)) ),
file('theBenchmark.p',sos_09) ).
fof(sos_11,axiom,
! [X14,X15,X16] :
( '>='(X14,X15)
=> '>='('==>'(X16,X14),'==>'(X16,X15)) ),
file('theBenchmark.p',sos_11) ).
fof(sos_12,axiom,
! [A] : '+'(A,'1') = '1',
file('theBenchmark.p',sos_12) ).
fof(sos_13,axiom,
! [A] : '==>'('==>'('==>'(A,'1'),A),A) = '0',
file('theBenchmark.p',sos_13) ).
fof(goals_14,conjecture,
! [X17] : '==>'('==>'(X17,'1'),'1') = X17,
file('theBenchmark.p',goals_14) ).
fof(goals_14_neg,negated_conjecture,
~ ! [X17] : '==>'('==>'(X17,'1'),'1') = X17,
inference(assume_negation,[status(cth)],[goals_14]) ).
cnf(c_16,plain,
'+'(A,B) = '+'(B,A),
inference(clausify,[status(thm)],[sos_02]) ).
cnf(c_17,plain,
'+'(A,'0') = A,
inference(clausify,[status(thm)],[sos_03]) ).
cnf(c_18,plain,
'>='(A,A),
inference(clausify,[status(thm)],[sos_04]) ).
cnf(c_19,plain,
( '>='(A,C)
| ~ '>='(B,C)
| ~ '>='(A,B) ),
inference(clausify,[status(thm)],[sos_05]) ).
cnf(c_20,plain,
( B = A
| ~ '>='(B,A)
| ~ '>='(A,B) ),
inference(clausify,[status(thm)],[sos_06]) ).
cnf(c_21,plain,
( '>='(B,'==>'(A,C))
| ~ '>='('+'(A,B),C) ),
inference(clausify,[status(thm)],[sos_07]) ).
cnf(c_22,plain,
( ~ '>='(B,'==>'(A,C))
| '>='('+'(A,B),C) ),
inference(clausify,[status(thm)],[sos_07]) ).
cnf(c_23,plain,
'>='(A,'0'),
inference(clausify,[status(thm)],[sos_08]) ).
cnf(c_24,plain,
( '>='('+'(A,C),'+'(B,C))
| ~ '>='(A,B) ),
inference(clausify,[status(thm)],[sos_09]) ).
cnf(c_26,plain,
( '>='('==>'(C,A),'==>'(C,B))
| ~ '>='(A,B) ),
inference(clausify,[status(thm)],[sos_11]) ).
cnf(c_27,plain,
'+'(A,'1') = '1',
inference(clausify,[status(thm)],[sos_12]) ).
cnf(c_28,plain,
'==>'('==>'('==>'(A,'1'),A),A) = '0',
inference(clausify,[status(thm)],[sos_13]) ).
fof(nnf_14,plain,
? [X17] : '==>'('==>'(X17,'1'),'1') != X17,
inference(fof_nnf,[status(thm)],[goals_14_neg]) ).
fof(sk_goals_14_neg,plain,
'==>'('==>'(sK0,'1'),'1') != sK0,
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X17,sK0)],[nnf_14]) ).
cnf(c_29,negated_conjecture,
'==>'('==>'(sK0,'1'),'1') != sK0,
inference(split_conjunct,[status(thm)],[sk_goals_14_neg]) ).
cnf(c_293,plain,
A = '+'('0',A),
inference(paramod,[status(thm)],[c_17,c_16]) ).
cnf(c_33,plain,
'+'('0',A) = A,
inference(copy,[status(thm)],[c_293]) ).
cnf(c_36,plain,
( '>='(A,'==>'(B,C))
| ~ '>='('+'(A,B),C) ),
inference(paramod,[status(thm)],[c_16,c_21]) ).
cnf(c_38,plain,
'>='('+'(A,'==>'(A,B)),B),
inference(resolve,[status(thm)],[c_22,c_18]) ).
cnf(c_294,plain,
'>='('+'(A,B),'+'('0',B)),
inference(resolve,[status(thm)],[c_24,c_23]) ).
cnf(c_40,plain,
'>='('+'(A,B),B),
inference(paramod,[status(thm)],[c_33,c_294]) ).
cnf(c_295,plain,
'1' = '+'('1',A),
inference(paramod,[status(thm)],[c_27,c_16]) ).
cnf(c_44,plain,
'+'('1',A) = '1',
inference(copy,[status(thm)],[c_295]) ).
cnf(c_64,plain,
'>='('1',A),
inference(paramod,[status(thm)],[c_44,c_40]) ).
cnf(c_76,plain,
'>='('==>'(A,'1'),'==>'(A,B)),
inference(resolve,[status(thm)],[c_26,c_64]) ).
cnf(c_296,plain,
'>='('+'('==>'('==>'(A,'1'),A),'0'),A),
inference(paramod,[status(thm)],[c_28,c_38]) ).
cnf(c_297,plain,
'>='('+'('0','==>'('==>'(A,'1'),A)),A),
inference(paramod,[status(thm)],[c_16,c_296]) ).
cnf(c_115,plain,
'>='('==>'('==>'(A,'1'),A),A),
inference(paramod,[status(thm)],[c_33,c_297]) ).
cnf(c_124,plain,
'>='(A,'==>'('==>'(A,B),B)),
inference(resolve,[status(thm)],[c_36,c_38]) ).
cnf(c_298,plain,
( '>='('==>'(A,'1'),C)
| ~ '>='('==>'(A,B),C) ),
inference(resolve,[status(thm)],[c_19,c_76]) ).
cnf(c_256,plain,
'>='('==>'('==>'(A,'1'),'1'),A),
inference(resolve,[status(thm)],[c_298,c_115]) ).
cnf(c_299,plain,
( A = '==>'('==>'(A,B),B)
| ~ '>='('==>'('==>'(A,B),B),A) ),
inference(resolve,[status(thm)],[c_20,c_124]) ).
cnf(c_300,negated_conjecture,
sK0 != '==>'('==>'(sK0,'1'),'1'),
inference(copy,[status(thm)],[c_29]) ).
cnf(c_291,negated_conjecture,
~ '>='('==>'('==>'(sK0,'1'),'1'),sK0),
inference(resolve,[status(thm)],[c_299,c_300]) ).
cnf(c_292,plain,
$false,
inference(resolve,[status(thm)],[c_291,c_256]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL902+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n003.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 23:49:08 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.37 % Process 1432633 was started by sandbox on n003,
% 0.08/0.37 % Fri Sep 25 23:49:08 2026
% 0.08/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.41
% 0.13/0.41 % SZS status Theorem for theBenchmark
% 0.13/0.41
% 0.13/0.41 % Proof 1 at 0.02 (+ 0.02) seconds.
% 0.13/0.41 % Length of proof is 37.
% 0.13/0.41 % Level of proof is 7.
% 0.13/0.41 % Maximum clause weight is 10.000.
% 0.13/0.41 % Given clauses 47.
% 0.13/0.41
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------